# Customers arrive at a ferry ticket office at the rate of 14 per hour on Monday morn-

## Question:

Customers arrive at a ferry ticket office at the rate of 14 per hour on Monday morn- ings. This can be described by a Poisson distribution. Selling the tickets and pro- viding general information takes an average of 3 minutes per customer and varies exponentially. One ticket agent is on duty on Mondays.

a. What is the average length of the line on Monday mornings?

b. On average, how long does a customer wait to buy a ticket on Monday mornings (in minutes)?

c. How long does it take to successfully buy a ticket on Monday mornings (in min- utes)? (This includes time waiting in line and purchasing from the agent.)

d. What is the probability that an arriving customer has to wait to buy a ferry ticket on Monday morning?

e. What is the probability of exactly four customers in the ferry ticket office? This includes both customers waiting in line and those being served.

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